A concentration function estimate and intersective sets from matrices
Abstract
We give several sufficient conditions on an infinite integer matrix (dij) for the set R = {Σij∈α, i>jdij: α ⊂ ℕ, {pipe}α{pipe} < ∞} to be a density intersective set, including the cases dnj = jn(1 + O(1/n1+ε)) and 0 < dnj = o(√n/logn). For the latter, a concentration function estimate that is of independent interest is applied to sums of sequences of 2-valued random variables whose means may grow as (√n/logn). © 2011 Hebrew University Magnes Press.
Publication Title
Israel Journal of Mathematics
Recommended Citation
Balister, P., & McCutcheon, R. (2012). A concentration function estimate and intersective sets from matrices. Israel Journal of Mathematics, 189 (1), 413-436. https://doi.org/10.1007/s11856-011-0176-4
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